Probably Linda (Continued)

The Linda Problem, which I discussed last time, is an illustration of how ordinary people do not engage in "right thinking." We are told the story of an imaginary woman, Linda, who was heavily into social justice and anti discrimination and you are asked which is more probable, that she is a bank teller or that she is a bank teller and a feminist. The correct answer is, in the world of probability theory, she is a bank teller. You are supposed to realize that adding the information she is a feminist reduces the probability, because there is a small chance that those characteristics which we associate with someone who might become a feminist does not guarantee she is a feminist. She might have been brought up in the Bible belt and while she shares some sympathies which are common among feminists, she does not embrace all the rest.

On the other hand, this whole problem hinges on your embracing the conventions of probability as it is taught in schools. What you are doing when you fail to think right, is you are going with "street knowledge" as opposed to what you've been taught in class, usually a class at some elite university or prep school. You have been schooled to think right.

But suppose we change the meaning of the word "probability" to the meaning it might have in the real world or say, the world of espionage. Suppose, for example, we are told the story of Linda, who has been tracked from her home in Russia to a training school in the elite Russian intelligence agency known to train sleeper agents who come to the United States, get ordinary jobs and ply their trade. Now I ask you the question: What is the greater probability A/ She is bank teller B/ She is a bank teller who is a Russian spy?

Now, of course, same rules apply by Dr. K's theory: She is a bank teller is the correct answer. It is possible she is not a Russian spy. The rest of the evidence is circumstantial and it is unproved she is working for the Russian spy agency which ran to the school, which got her her visa and provided her money, car and home. There is a small, however small chance, she is not a spy. She may have rejected all that training and just enjoys life in America as a bank teller. The chances may be small she is not a spy, but the chances are not zero.

On the other hand, if you are watching this on TV, or on the jury, while you understand more evidence is needed and you understand the chances are not 100% she is a spy, you know the greater probability is she is a bank teller (which is irrelevant, given the totality of the information you have been given) and a spy than the probability she is simply a bank teller.

If we had a jury of engineers, math majors and Ivy League graduates she might be set free. If we had a Baltimore jury, she's a spy.

Who is thinking more right, now?